Question 151299
{{{8/x-5/y=51/14}}} Start with the first equation.



{{{14xy(8/cross(x)-5/cross(y))=14xy(51/cross(14))}}} Multiply both sides by {{{14xy}}}. This will eliminate the fractions.



{{{112y-70x=51xy}}} Distribute and multiply



{{{-70x=51xy-112y}}} Subtract {{{112y}}} from both sides.



{{{-70x=y(51x-112)}}} Factor out {{{y}}} from the right side.



{{{(-70x)/(51x-112)=y}}} Divide both sides by {{{51x-112}}}.




So after isolating y of the first equation, we get {{{y=(-70x)/(51x-112)}}}




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{{{6/x+(-10)/y=-(29/7)}}} Move onto the second equation



{{{6/x+(-10)/((-70x)/(51x-112))=-(29/7)}}} Plug in {{{y=(-70x)/(51x-112)}}}. In other words, replace "y" with {{{(-70x)/(51x-112)}}}



{{{6/x+(-10)((51x-112)/(-70x))=-(29/7)}}} Multiply the numerator "-10" by the reciprocal of the fraction in the denominator.



{{{6/x+(-510x+1120)/(-70x)=-(29/7)}}} Distribute



{{{6/x+(510x-1120)/(70x)=-(29/7)}}} Simplify.



{{{70x(6/cross(x)+(510x-1120)/(cross(70x)))=70x(-(29/cross(7)))}}} Multiply both sides by {{{70x}}}. This will eliminate the fractions.



{{{420+510x-1120=-290x}}} Simplify



{{{420-1120=-290x-510x}}} Subtract {{{510x}}} from both sides.



{{{-700=-800x}}} Combine like terms.



{{{(-700)/(-800)=x}}} Divide both sides by -800.



{{{x=7/8}}} Reduce. So this is the first part of the answer.



{{{y=(-70x)/(51x-112)}}} Go back to the first isolated equation



{{{y=(-70(7/8))/(51(7/8)-112)}}} Plug in {{{x=7/8}}}



{{{y=(-245/4)/(357/8-112)}}} Multiply and reduce



{{{y=(-245/4)/(-539/8)}}} Subtract



{{{y=(-245/4)*(8/(-539))}}} Multiply the first fraction by the reciprocal of the second fraction.



{{{y=10/11}}} Multiply and reduce




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Answer:


So the answer is {{{x=7/8}}} and {{{y=10/11}}} which forms the ordered pair *[Tex \LARGE \left(\frac{7}{8},\frac{10}{11}\right)]